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Directivity at Industrial Sources

When sound sources are not radiate uniformly in all directions, this can be accounted for by selecting a pre-defined directivity or by entering a user-defined directivity. The calculation procedure selected for industrial noise (see Standards) specifies on how to consider directivity within the calculation of sound propagation. However, the majority of the calculation procedure for industrial noise do not specify much detail on input and application of directivity data. The following statements refer, as an example, to the application of directivities in conjunction with ISO 9613-2.

Directivity with ISO 9613-2

The equation (3) in ISO 9613-2 (1996) ISO-9613-2-2024 introduces the directivity correction Dc:

\(L_{fT}(DW)=L_W+D_C-A\)

with

  • \(L_{fT}(DW)\): energy-equivalent continuous sound pressure level for downwind in octave band width, in dB

  • \(L_W\): sound power level in octave band width of the point source, in dB (reference sound power (10-12 W)

  • \(D_C=D_I+D_\Omega\): directivity correction in dB, where \(D_I\) is the directivity index of the point source and \(D_\Omega\) is the correction for sound radiation into solid angles smaller than 4π steradians

  • \(A\): total attenuation per octave band occurring on the propagation path, in dB

According to the equation for LFT(DW), the directivity correction is added to the sound power level. This requires that the directivity itself must be normalized to a sum level of zero dB, in order not to alter the sound power radiated by the point source. More details for input or application of directional effects cannot be found in ISO 9613-2.

This statement also applies for other standards and procedures for industrial noise.

Note

When modeling road, railway or aircraft noise directional effects may also be considered on the source-side within the calculation of sound propagation. In these cases, however, the directivities applied form an integral part of the source description and can, therefore, not be modified by the user.

Directivity dialog

The Directivity dialog is accessed via the button „Directivity“ on the source dialogs of industrial sources (point, line, area sources).

Dialog Directivity

A selected directivity is indicated by a check mark on the "Directivity" button in the source dialog after closing the Directivity dialog.

Dialog options

List box „Directivity“

In order to account for non-uniformal sound radiation of industrial sources two types of directivities are available:

Example

Path: Examples\Infos\Tunnel

Example

Path: Examples\Infos\Recreational Noise

  • line arrays, type „flown low“, accord. to table 12 of the “Supplement to the Saxonian study on noise from recreational activities” (translated from German title, 2019) Ede-2019
  • line array, type „flown high“, see Ede-2019
  • user-defined directivities: Individual, frequency-dependent directivities can be defined via the menu Tables|Libraries (global) or (local)|Directivity (see User-defined Directivities). When user-defined directivities have been entered, their name will appear at the end of the list box „Directivity“ on the Directivity dialog.

Option „Automatic Direction“

With this option (default setting), the normal direction (0°) of the selected directivity for point sources will point into the normal direction of a nearby building facade. After calculation, the coordinates of the directivity vector are shown into the corresponding input boxes „xyz“.

Automatic orientation depending on source type

The orientation of the directivity vector depends on the type of industrial source. The following strategies are applied:

source type orientation of the directivity vector picture
point source
 The directivity vector is pointing into the normal direction of the nearest building facade, within a 1 m radius of the point source. When no facade is found, the directivity vector is pointing into
+z direction (independent of the source height).
vertical cross section
The directivity assigned points into positive z direction (z=1), since the ground is seen as a reflection surface.
line source
 The directivity vector is pointing from the first to the last polygon point (for each segment of the line source).
The resulting level distribution results from assigning the directivity selected to each segment of the line source.
top view
area source
 The directivity vector is pointing into the normal direction of the area source.
The resulting distribution results from assigning the directivity to each point-like sub-source within the borders of the area source.
vertical cross section
vertical area source
 The directivity of vector is pointing to the right, seen from the first to the last point.
Consequently, enter vertical area sources at buildings counterclockwise!
top view

Note

The automatic orientation of directivity vector for point sources only occurs nearby, reflecting worldwide, not with reflective screens or cylinders.

Option „Vector“

When activating this option the directivity vectors 1 and 2 can be individually oriented by entering the coordinate directions xyz. The figures entered will be normalized after calculation to the unit circle (radius R=1, x2 + y2 + z2=1).

Examples:

Coordinates (x,y,z) Directivity vector is pointing towards the direction ...
Vector 1 Vector 2
(1, 0, 0) (0, 0, 0) ... of the positive x-axis (i.e. to the "right").
(0, 0, 1) (0, 0, 0) ... of the positive z-axis (i.e. "upwards")..
(1, 1, 0) (0, 0, 0) ... the bisecting line between the positive x and the positive y axis (at 45 degrees, to the „right upper corner“).
After a calculation the vector coordinates are normalized to the unit circle, in this case (x, y, z) = (0.7071, 0.7071, 0) [R=sqrt(0.7071^2+0.7071^2)].

Option „Rotation Angles“

Enter alternatively the rotation angles which the directivity vector forms with the respective coordinate axis:

  • phi φ: angle of rotation of the directivity vector 2 (in the figure: x') about the +z axis (i.e. in the xy plane)
  • theta ϑ: angle of rotation of the directivity vector 1 (in the figure: z') about the +z axis
  • psi ψ: angle of rotation about the positive axis of the directivity vector 1 (in the figure: z ')

Angles phi φ, theta ϑ and psi ψ

Appearance of directivity of point sources

The following options are available for displaying the directivity in the model:

  • 2D view: In the appearance menu an additional layer can be defined, which shows, depending on the main direction DIR_ANGLE, for example an arrow. For this purpose, a layer is already included in the default appearance of CadnaA, which must be activated for the representation "on Screen" and/or "on Paper".
  • 3D view: In the appearance menu in the 3D tab, the option " Show directivity" can be activated. With this option, the directivity balloon is also displayed in the 3D special view.

Button „3D“

Opens a 3D dialog showing a directivity balloon. For handling details see User-defined Directivities.

Since inputting vector coordinates or rotation angles may not be intuitively accessible, the easier way is to orientate the directivity in 3D by rotating it as needed using the mouse. Press the SHIFT key, when you stop dragging the values in the dialog will get updated. There is always a 1:1 relation between the two vectors and the rotation angles.

Exhaust Velocity (m/s), Exhaust Gas Temperature (°C), Wind Speed (m/s)

are required to calculate the chimney's directivity according to VDI-guideline 3733.

Further information

Interpolation when applying directivity

When evaluating of user-defined directivities (via menu Tables|Libraries (local)|Directivity) to ray paths the following step apply:

  • For each ray (source-receiver) or (source-first reflector, see below) the angle to North direction is determined.
  • Depending on the directivity vector and the ray‘s direction the relevant directivity correction is determined for each ray. For ray directions between two angular steps of 15° (see User-defined Directivities) the directivity correction results from linear interpolation.
  • The directivity index \(D_I\) is added to the correction for solid angle \(D_{\Omega}\) - if any - and considered as \(D_C\) in the calculation of propagation (see Calculation Protocol).

Directivity at reflected rays

The calculation procedures - e.g. also not ISO 9613-2 - do not specify how to handle the directivity correction in conjunction with the reflected rays. In CadnaA, the following strategy is used:

  • In case of reflected rays - independent of the reflection order - the first section of the ray (from the source to the 1st reflector) determines the direction being used to evaluate the relevant directivity correction.
  • This directivity correction is used, even if the ray, possibly after multiple reflections, arrives at the receiver from a different direction.